Whoever the primary tax payer is. If your husband is listed as the primary tax payer, then you will use his social security number to check the status of refund.
If your federal return is accepted by the IRS, use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
If your state return is accepted, use
this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund