Can husband and wife both receive social security?

Yes. See the following excerpts from the Social Security website at the related link provided below:

Spouse's benefits:

A spouse who has not worked or who has low earnings can be entitled to as much as one-half of the retired worker's full benefit. If you are eligible for both your own retirement benefits and for benefits as a spouse, we always pay your own benefits first. If your benefits as a spouse are higher than your retirement benefits, you will get a combination of benefits equaling the higher spouse benefit.

If you have reached your full retirement age, and are eligible for a spouse's or ex-spouse's benefit and your own retirement benefit, you may choose to receive only spouse's benefits and continue accruing delayed retirement credits on your own Social Security record. You may then file for benefits at a later date and receive a higher monthly benefit based on the effect of delayed retirement credits.

If you are receiving a pension based on work where you did not pay Social Security taxes, your spouse's benefit may be reduced.

Benefits for a divorced spouse

Your divorced spouse can get benefits on your Social Security record if the marriage lasted at least 10 years. Your divorced spouse must be 62 or older and unmarried.

The amount of benefits he or she gets has no effect on the amount of benefits you or your current spouse can get.

Also, if you and your ex-spouse have been divorced for at least two years and you and your ex-spouse are at least 62, he or she can get benefits even if you are not retired.