Not on TD status, which allows study but no employment. He would need his own route, and paramedic is not a listed TN profession. Assess whether any of his qualifications fit a listed occupation before assuming a second income.
TD is a place to live, not a permit to work
Dependants of a TN professional enter in TD status, which permits residence and study but not employment of any kind, paid or volunteer-for-compensation. A spouse whose occupation is not on the USMCA list cannot simply switch to TN in his own right. Paramedic does not appear in Appendix 2, so a spouse in that role would need to look elsewhere: a different listed profession he is qualified for, an employer willing to sponsor another category, or a decision to defer his U.S.
work until the household's situation changes. The practical step is to lay out his education and licences and check each against the list before the family budgets on two salaries. Children in TD status can attend school without a separate student visa, but they too cannot work, and they lose TD status at 21 regardless of the parent's continued employment.
Hypothetical example: A labour-and-delivery nurse plans to relocate with a spouse who repairs string instruments from home. The household should not treat that private client work as harmless while the spouse has TD status; the question is whether the activity is employment, not where the customer is located. A first review produces a budget separating the nurse's expected income from any work the spouse must defer, plus a list of the spouse's credentials for an independent immigration assessment.
The marriage certificate and each child's birth record settle derivative eligibility. A missing relationship record can delay the family even when the principal nurse's package is complete.