Using HSA to pay for spouse and son's medical expenses if they're covered under a different HDHP w/ HSA

My wife and I both have health plans requiring spouse to be covered by their own employer's medical plan if they offer one. So, we each have our own HDHP and associated HSA accounts. In February we had our first child and he was added to my wife's health insurance. With all of the deductible and out of pocket max being billed to us, am I allowed to use MY HSA account to pay for their bills or am I not allowed due to them being covered by her health plan and HSA?