Your batteries contain limited power, Thus the inverter (Which is likely a fairly small one) can not power EVERYTHING, Many factory inverters run only the "Electronics" (Radio/TV and associated stuff) Soem also power the Microwave, Mine is an after market and powers the above PLUS the GFCI chain.
Very very few Motor homes have "whole house" inverters, (This would need to be in the range of 3000 to 5000 watts or more and need at least one pair of GC-2 batteries or one 8-D 12 volt per kilowatt of power).
So, what you saw is normal operation.
