Aww that is so sweet that your DH cares for you so much and is so protective to the put that it's going a bit over the top... he is probably feeling very anxious like you said, perhaps just talk to him and let him know you are coping just fine and that if anything was to happen whilst you were home and he was at work, that you'd call him and he would know about it....

My DH is really relaxed about all this... it's our first bub too. I think because my Dh is a registered nurse too probably helps as medical stuff, pregnant women etc doesn't scare him he's seen it all before but for most husbands it's all very new.... remind your husband that you aren't 'sick' you're just 'pregnant' and that it's a natural thing for a woman and her body to go through

Just talk to him and let him know it's all okay and that he should be saving his energy for the labour/birth as he'll need it then!!