Depending on your inverter/charger's size (how many amps of charging available), you may have to go in and reduce the amps of 120 VAC it can use. Often called "power share/power save". This can be done in a few seconds from your inverter/charger remote.
Obviously, verify that all other 120 VAC loads are OFF. If residential refrigerator tries to start and inverter/charger is in high-amp bulk mode, you may be exceeding the Honda's capability. If this happens, might turn off the refrigerator breaker until charge amp rate tappers off a little.