I assume you have American Power. I don't really understand how how US power phases cooperate with each other but I know you have 2 live wires coming into your house and the 120V regular power to outlets/lights can be spliced off either one.

It takes a combination of both live/phase wires and the ground to make 240V for higher power applications such as a washing machine/dryer.

If half of your house is missing power, either the corresponding breaker/GFGI or straight up conductor (wire) have an internal problem and need replacing OR that particular half of the house is spliced off one of the phases/lives and that particular live/phase has a problem in the grid and you're not receiving full power.

Makes sense to not splice the entire house 120v into only one phase as to not load the grid too much on a phase while the rest idle ... in EU that's balanced between households but that's not important....