This page has been updated for 2018 taxes and may not apply to previous years.
For federal returns, no. You must both itemize your deductions or you must both take the standard deduction.
For example, if you and your spouse file separate returns and your spouse claims itemized deductions, you must also claim itemized deductions. This is the case even if your standard deduction is higher than your itemized deductions.
State returns may have different rules and can vary by state.