A. Community debts shall be satisfied first from all community property and all property in which each spouse owns an undivided equal interest as a joint tenant or tenant in common, excluding the residence of the spouses. Should such property be insufficient, community debts shall then be satisfied from the residence of the spouses, except as provided in Subsection B of this section or Section 42-10-9 NMSA 1978. Should such property be insufficient, only the separate property of the spouse who contracted or incurred the debt shall be liable for its satisfaction. If both spouses contracted or incurred the debt, the separate property of both spouses is jointly and severally liable for its satisfaction. B. Unless both spouses join in writing in the creation of the underlying debt or obligation incurred after the marriage, a judgment or other process arising out of such post-marital debt against one spouse alone or both spouses shall not create a lien or otherwise be subject to execution against the interest of the nonjoining spouse in the marital residence, whether held by the spouses as community property, joint tenants or tenants in common. C. The priorities or exemptions established in this section for the satisfaction of community debts must be claimed by either spouse under the procedure set forth in Section 42-10-13 NMSA 1978, or the right to claim such priorities or exemptions is waived as between a spouse and the creditor. D. This section shall apply only while both spouses are living and shall not apply to the satisfaction of debts after the death of one or both spouses.