Sleeplessness is tough right now. It clouds your judgement and befuddles your whole day. Once you have established there is no physical problem and if your little guy is nursing, the answer is simple, take him to bed with you and nurse him right back to sleep. I've done this with my children and we are all happier.
If your little guy is bottle fed, he is possibly sensitive to the formula, if it's dairy based, you may want to try soy or goat's milk, as it's much less antagonistic to their new digestive system. Babies are not devious and are pretty clear about what they need, so Baby just wants the touch and support of mom or dad. The 'let them cry' method is no longer as popular as once thought, as it ultimately is sending the message that their needs are not important, and everyone is suffering. Right now,is a very short amount of time, compared to a very long and healthy life, so it's not that bad to keep them with you at night, for this short while. It's been done all over the world for generations, 'the family bed'.
If both parents do not agree on this method, maybe you could put baby next to your side of the bed, in a bassinet, or whatever works for you, so that all you have to do is reach over and cuddle or touch baby to let them know you are near, before they wake up completely.
When they are in another room entirely, they have been awake awhile and crying, usually, before you have woken up and heard them and in that amount of time, it has escalated into a high anxiety situation for your baby. Nearer to your reach may make it easier for baby and you as well.
References: The Womanly Art of Breastfeeding book has some good parenting techniques in it, as well as Dr. William Sears book The Baby Book: Everything You Need to Know About Your Baby from Birth to Age Two (Key Phrases: healthy sleep attitude, nighttime parenting styles) might help give you the support and confidence you need right now.
This will all be better, soon. Good Luck.