Bottom line up front: You're looking for Command Query Responsibility Segregation; which defines an architectural pattern for breaking up responsibilities from querying for data to asking for a process to be run. The short answer is you do not want to mix the two in either a query or a process in a blocking fashion. The rest of this answer will go into detail as to why, and the three different ways you can do what you're trying to do.
This answer is a short form of the experience I have with Microservices. My bona fides: I've created Microservices topologies from scratch (and nearly zero knowledge) and as they say hit every branch on the way down.
One of the benefits of starting from zero-knowledge is that the first topology I created used a mixture of intra-service synchronous and blocking (HTTP) communication (to retrieve data needed for an operation from the service that held it), and message queues + asynchronous events to run operations (for Commands).
I'll define both terms:
Commands: Telling a service to do something. For instance, "Run ETL Batch job". You expect there to be an output from this; but it is necessarily a process that you're not going to be able to reliably wait on. A command has side-effects. Something will change because of this action (If nothing happens and nothing changes, then you haven't done anything).
Query: Asking a service for data that it holds. This data may have been there because of a Command given, but asking for data should not have side effects. No Command operations should need to be run because of a Query received.
Anyway, back to the topology.
Level 1: Mixed HTTP and Events
For this first topology, we mixed Synchronous Queries with Asynchronous Events being emitted. This was... problematic.
Message Buses are by their nature observable. One setting in RabbitMQ, or an Event Source, and you can observe all events in the system. This has some good side-effects, in that when something happens in the process you can typically figure out what events led to that state (if you follow an event-driven paradigm + state machines).
HTTP Calls are not observable without inspecting network traffic or logging those requests (which itself has problems, so we're going to start with "not feasible" in normal operations). Therefore if you mix a message based process and HTTP calls, you're going to have holes where you can't tell what's going on. You'll have spots where due to a network error your HTTP call didn't return data, and your services didn't continue the process because of that. You'll also need to hook up Retry/Circuit Breaker patterns for your HTTP calls to ensure they at least try a few times, but then you have to differentiate between "Not up because it's down", and "Not up because it's momentarily busy".
In short, mixing the two methods for a Command Driven process is not very resilient.
Level 2: Events define RPC/Internal Request/Response for data; Queries are External
In step two of this maturity model, you separate out Commands and Queries. Commands should use an event driven system, and queries should happen through HTTP. If you need the results of a query for a Command, then you issue a message and use a Request/Response pattern over your message bus.
This has benefits and problems too.
Benefits-wise your entire Command is now observable, even as it hops through multiple services. You can also replay processes in the system by rerunning events, which can be useful in tracking down problems.
Problems-wise now some of your events look a lot like queries; and you're now recreating the beautiful HTTP and REST semantics available in HTTP for messages; and that's not terribly fun or useful. As an example, a 404 tells you there's no data in REST. For a message based event, you have to recreate those semantics (There's a good Youtube conference talk on the subject I can't find but a team tried to do just that with great pain).
However, your events are now asynchronous and non-blocking, and every service can be refactored to a state-machine that will respond to a given event. Some caveats are those events should contain all the data needed for the operation (which leads to messages growing over the course of a process).
Your queries can still use HTTP for external communication; but for internal command/processes, you'd use the message bus.
I don't recommend this approach either (though it's a step up from the first approach). I don't recommend it because of the impurity your events start to take on, and in a microservices system having contracts be the same throughout the system is important.
Level 3: Producers of Data emit data as events. Consumers Record data for their use.
The third step in the maturity model (and we were on our way to that paradigm when I departed from the project) is for services that produce data to issue events when that data is produced. That data is then jotted down by services listening for those events, and those services will use that (could be?) stale data to conduct their operations. External customers still use HTTP; but internally you emit events when new data is produced, and each service that cares about that data will store it to use when it needs to. This is the crux of Michael Bryzek's talk Designing Microservices Architecture the Right way. Michael Bryzek is the CTO of Flow.io, a white-label e-commerce company.
If you want a deeper answer along with other issues at play, I'll point you to my blog post on the subject.
