Ordinary vs. General

I also think general sounds strange there, and would prefer the word ordinary. General would be understood, but your listener would probably pause for a moment upon hearing it.

The word general is not synonymous with the word ordinary. As such, they cannot be used interchangeably.

An ordinary household is a typical or every-day one that is neither rich nor poor, neither spectacular nor bland.

There is no meaning or usage I might give you for a general household as it is not something an English-speaker might commonly refer to.

The word typical or average would also work.