You said your husband had been seeing this dentist on a regular basis, which "implies' he went at a minimum of 2 times and guessing at least 3 to 4 times to accumulate $6,000 in dental bills.
Most dentists like doctors, will submit bills every month of what you owe. So, my guess you should have received at least 1 or maybe 2 bills stating you owe so much, and you could have ignored them "thinking" that no insurance shown, and waiting til you find out how much insurance pays (before) you pay the balance.
Proving your husband as a dependent? huh? Most health insurance with employers is employee with (spouse) or spouse with child/s. Is it because you did not have health insurance last year that you had to prove he had or not?
Now, when I was employed (retired) then when I enrolled with my employers health, dental etc, then I usually got a copy back of (what) I chose, and usually with that would list how much (each) paycheck the amount that would be deducted for each. I do remember my paychecks listing (separately) the amount for health and the amount for dental.