Mortgage or rent in both places, insurance that reflects how the Canadian home is occupied, property management if there are tenants, and travel between the two. None of it is an immigration cost, but it shapes whether the assignment is workable.
Cost the whole arrangement before committing
Set out the ongoing Canadian costs alongside the US housing the assignment requires, and ask the employer what relocation or housing support is offered and on what conditions. Insurers often treat a vacant or tenanted property differently from an owner-occupied one, so confirm coverage before leaving. Get any employer contribution and its reimbursement conditions in writing.
The recurring cost is the health-care certification and state licence, not the immigration fee. A lease term that outlasts the current TN period creates its own risk, since renewal is not guaranteed even though extensions remain genuinely possible while the underlying work and profession continue to qualify. Ask the employer how far in advance the petition or admission request will be handled relative to any lease renewal deadline, so a housing commitment does not outrun the status decision. Selling the Canadian home versus renting it out carries immigration relevance too: keeping a residence available in Canada can support the temporary intent TN status requires, while severing every tie may invite questions about that same intent later. Currency exchange on rent or mortgage payments, cross-border tax filing for two residences, and the cost of maintaining a vacant property belong in the same budget as the immigration filing itself. Get a written understanding of who handles each of these decisions before signing a new lease in the United States.