Hmmm. I don't have any experience with the military aspect of your life, nor of a DH/father who works away from home. Neither do I have any experience of not minding being left along holding the babies (we're pretty much split 50/50 in terms of family and house duties). HOWEVER, I don't think I could be the one to stand between someone and their passion/life's calling/fulfillment. Least of all my DH who is my best friend, and who I love dearly and want the best for. I would find a way to make it happen.
Your children are young, you have time. Can you arrange for you to take the children to visit your family and friends in your home country while he goes on this expedition? Or for someone to come and stay while he's away, just to be a distraction for you and the DC, to break up the monotony?
My DC are older than yours and they would be beyond thrilled for their Dad to be climbing Everest (or whatever). It would be an all-family project, we'd all be into the planning and the talking and and the build-up etc. It doesn't interest me in the slightest, but I would 100% support my husband or my children in facilitating such a thing. My DH would also totally support me if I ever asked, probably down the line when children are older, to leave the DC with grandparents to go to Fiji on a lazy beach trip with him, even if he didn't particularly want to. It's give and take.
Another option, although your DC are quite young for this, if for you all to go as my friend did. The whole family went to Everest base camp, her DH and FIL tried to summit (inclement weather, it didn't happen). It was an amazing experience for them all.
Ultimately, what your DH is saying is that he wants fulfillment in his life. Everybody deserves that, you too. In a partnership, people help each other achieve that. It doesn't have to be expeditions, it doesn't have to be equal to the penny and the day, everyone has their thing.