Would you be comfortable if your husband carpooled with a women you didn't know?

Back story:

Two weeks ago my husband started a new job, the second day he carpooled with a man who has been at the job for some time and an intern, the women. That night we talked about it and i told him i thought the carpool thing was great however not appropriate for him to do so with just her, he agreed.

Yesterday he drove her, alone and i didn't know until late last night when it randomly got brought up... and the weird thing was her dad apparently dropped her off at our house and he told my husband, "I'm going to have to do a background check on you." Weird, right?! As if they were dating?

I'm pregnant and not sure if my hormones are a factor but i don't think a married man should carpool with a single younger women.

(Side note, my husband would never be okay with me driving with another man.)