Is my ex-domestic partner responsible for at least half of the debts that we acquired over the last20 years?

Unfortunately, domestic partnerships have not been legally recognized for a long time and if you have acquired expenses over the past 20 years, you may be out of luck.  Unless you can prove that you had an agreement and he has paid consistently over the past twenty years, simply having him as a secondary may not be sufficient evidence he was to pay for half of the expenses.  Even if you had an agreement, most contract laws (especially in California) have a statute of limitations.  The statute of limitations tells you how long you have to enforce an agreement.  The most I have seen is three or four years, not twenty.  This means you may not be able to collect for expenses incurred so long ago but may have a chance for expenses incurred from two or three years ago.  If you can show he paid for at least one month, you can make the argument that he was not gifted those amounts but rather it was either a loan or an agreement to share the expenses.

Generally speaking you are not responsible to pay the debts on credit cards where you arenot the original applicant to the card.  When you say that he is the "secondary" cardholder so you mean that you both applied and are listed as cardholders with the credit card company or is he only an "authorized user" on the account?  Authorized losers get a free pass, unfortunate as that can be.  Applicants directly to the card lender and who signed the agreement can be held accountable.  Do you have the original paperwork for the account?  Can you call the card and find out now?  Ask for a copy of the original agreement.  That will let you know.  Then you will know how to proceed in the matter.  Good luck.