Hi - yes, simultaneous use of the AC and DC power is possible, but wattage should not exceed the rated output.
It should also be noted that the DC charge from the generator is not regulated and is mostly designed for 'just in case' situations, i.e. your flat car battery needs a short trickle charge. For full charging of your batteries, you should always use a quality battery charger which connects between the AC output on the generator and your batteries - this will ensure safe and efficient charging of your batteries.
Thanks.