I do not know what exactly you would like to achieve so if my answer will be in a wrong direction we can elaborate more.
I used this code to produce a map with contourfm
and 'landareas'
:
load geoid;
figure(1)
axesm ('mercator','MapLatLimit',[-50 90],'MapLonLimit',[0 250])
contourfm(geoid,geoidrefvec, 'LineStyle', 'none');
geoshow('landareas.shp', 'FaceColor', [0.5 1.0 0.3]);

Instead of geoid
you can have your own map but pay attention on the number of grid points. As far as I know they have to be 180x360.
One note. You may consider to use coast
in stead of landareas
because contourfm
produces all colour map and 'landareas'
has also colours. So if it suit you, you can put only coast lines instead:
load geoid;
figure(2)
axesm ('mercator','MapLatLimit',[-50 90],'MapLonLimit',[0 250])
contourfm(geoid,geoidrefvec, 'LineStyle', 'none');
load coast
plotm(lat, long,'black') % plot the coast on the map