One thing you might not realize...in an HDHP you have to hit the family deductible before coverage starts. So if the single deductible is 3000 and the family deductible is 6000, you will have to pay out the whole 6000 even if only one person has claims.
In other plans, each individual usually has a deductible and two people would have to have claims in order to ever get to the family deductible.
So if your wife takes the individual plan, she would have the 3000 deductible, but you and the kids would still have the 6000 deductible.
I don't believe that's true.
My understanding is that the following math is true:
Family consists of Bob, Jane, Stan, and Mary.
Scenario A
Bob spends $2300. All of that is applied to his deductible and all of that is applied to the family deductible.
Jane spends $500, All of that is applied to HER deductible. And all of that is applied to family deductible.
Stan spends $3000. His deductible is now maxed. But the total family deductible is still only: $5800.
So, when Mary spends another $600. The first $200 is applied to the family deductible, which is now maxed at $6000, and the rest of the $400 is paid under the plans provisions.
Scenario B
Bob spends $2800. All of that is applied to his deductible and all of that is applied to the family deductible.
Jane spends $500, All of that is applied to HER deductible. And all of that is applied to family deductible.
Bob needs a bit more stuff, $1200 more of medicine. The first $200 is applied to his deductible taking it to the max $3000, and the rest of the $1000 is paid for under the plans provisions. (I'm a little fuzzy if any kind of copayments would count toward the family deductible still). Family deductible is: $2800 + 500+200+(copayments??) = 3500
Stan spends $3000. The family deductible max of $6000 is hit with the first $2500 of his expenses. The rest of the $500 would be paid for by the plan.
So, In this case, doesn't matter what Mary spends, since the family deductible is maxed out, her stuff is covered.
But yes, if my wife had a separate plan, she'd have to meet her deductible and non of her contributions would apply towards me and kids in the other plan. Nor vice versa.
Follow up questions
Is there any way for an employer to prevent you from moving dollars out of an HSA into another 3rd party HSA?
And if my employer contributes $2400 to my HSA, and $1200 to my wife's HSA, then we can contribute (in total) $7100-$3600 = $3500 as qualified HSA contributions??