It's not abnormal - lots of babies do it. But it can be very exhausting!
Try and teach him about daytime - lots of light, getting out and about, and encouraging him to feed more and more during the day. Sleep when he sleeps during the day (screw the housework - sleep is more important). Especially encourage cluster feeding before putting him down for the night (a few feeds close together), so he lasts a bit longer. Then go to bed yourself, because that period is likely to be his longest sleep.
For most full term babies things improve between 6 and 12 weeks - so that probably starts about now for you.