My husband (67) and I (62 in 3/17) have both worked and are both entitled to social security on our own. My husband has not yet filed. We were both married to our ex-spouses for over 10 years and both ex-spouses are already at full retirement age, although neither has yet filed. If we both file in March 2017 for divorced spousal benefits, does this preclude use from filing for our own benefits when we turn 70, respectively?

k,
Your husband can file for divorced spouse's benefits without affecting his ability to delay his retirement benefit since he's over his full retirement age (FRA). However, since you were born after 1 Jan 1954, when you file for divorced spouse's benefits you will be deemed by law to have also filed for your retirement benefit at that time. So, if you want to delay your retirement benefit until age 70, don't file for divorced spouse's benefit before then.
Best,
Mike