Swift variable that conforms to type and protocol

Question

How can I have a variable in Swift that has the following restrictions:

1. It must conform to a specific protocol
2. It must be a subclass of UIView
3. It does not need to be a direct subclass child of UIView (i.e. it may be a subclass of a UIButton, for example)

Note that this is similar to this (which fails to satisfy point 3).

The following also satisfies points 1 and 2 (but not 3):

protocol MyProtocol {
    var onClick: Void -> Void {get set}
}

class MyCommonView: UIView, MyProtocol {
    var onClick: Void -> Void = {
        println("onClick!")
    }
}

class MyLittleView: MyCommonView {

}

class MyBigView: MyCommonView {

}

var myView: MyProtocol!
myView = MyLittleView()
myView.onClick()
myView.backgroundColor = UIColor.redColor()  // 'MyProtocol' does not have a member named 'backgroundColor' 

myView = MyBigView()
myView.onClick()
myView.backgroundColor = UIColor.redColor()  // 'MyProtocol' does not have a member named 'backgroundColor' 

Edit Although this is similar to this question (and answer by @zneak), it would be great to not have to specify all the UIView methods that I want to use, I'd like to be able to use any or all of them.

Here is what I came up with based on the answer given by @zneak, can it be improved so as not to have to specify all the needed UIView methods I want to use?

protocol MyOnClickProtocol {
    var onClick: Void -> Void {get set}
}

protocol MyViewProtocol {
    var backgroundColor: UIColor? {get set}
    // And other methods or properties of UIView that I want to access...
}

class MyLittleView: UIButton, MyOnClickProtocol, MyViewProtocol {
    var onClick: Void -> Void = {
        println("onClick!")
    }
}

class MyBigView: UISwitch, MyOnClickProtocol, MyViewProtocol {
    var onClick: Void -> Void = {
        println("onClick!")
    }
}

var myView: protocol<MyViewProtocol, MyOnClickProtocol>!
myView = MyLittleView()
myView.onClick()
myView.backgroundColor = UIColor.redColor()

myView = MyBigView()
myView.onClick()
myView.backgroundColor = UIColor.redColor()