Probably not a good idea or at best marginal.
If you have a 750 watt microwave, you'd think that means it only needs 3 amps - but that's the output (cooking) power of the microwave and not the input power which will be 1000 watts or more (1000 watts = 4 amps).
But also remember that the fridge will be on drawing 120 watts, plus the battery charger, and anything else you have switched on.
So it's my belief that a medium rated microwave - in conjunction with other stuff you'll have running - will trip or be very close to tripping the power.
At one site, our fridge and a 500 watt kettle (maximum of 3 amps combined) tripped the 4 amp pole switch in France.
Robert