So. be sure he is not basing his request for a DNA test on a false notion that if the doctor says "You're 8 weeks pregnant," that means you're 8 weeks since conception. Because if a doctor said that, he would mean you're around 6 weeks since conception.
Regarding the DNA test, the hospital can take the samples from you and your husband and the baby, when the baby is born. The swabs will need to be sent to a lab that does paternity testing. This is arranged by you in advance, so if the above does not cause your husband to stop worrying, and if your doctor telling him this does not calm him down, talk to your doctor. to arrange the test.
If his problem is simply the timeline, do you know (and did you tell him) that doctors do not begin the "weeks" count on the day of conception? They begin it on the first day of the woman's last period that she had before getting pregnant, which is usually at least a couple of weeks prior to when the baby would have been conceived. And if the woman's cycle is irregular, conception can be even later than two weeks from the first day of the last period.
In case this concept is unfamiliar to you, it happens because back in the day, there were no ultrasounds. The only signal a doctor had to begin any kind of count was noting the date when the woman began her last period. Of course, even then doctors knew a woman does not get preggers on the first day of her period -- she is bleeding, not ovulating! But it was the only thing they had to use as a starting point. So, they figured out they could begin the count then, and allow a two-week time period to be the gap between the first day of the period and the assumed ovulation date.