Husband and Wife traveling on separate air tickets

Hi IL's,

My husband and I are travelling to and from on the same dates but we both have separate air tickets.
My ticket is me and my kids and his ticket is just him.

I wanted to know if this is considered as not traveling as a Family ?
When asked at the Customs in the US should we say we are traveling alone since we have separate tickets ?
Are we both then entitled to each bring in $10K worth of monetary items without having to declare ? Him 10K and me 10K.

Thanks in advance for your suggestions.