You're misunderstanding. I am saying that you can successfully argue that faith CAN BE (not necessarily that any particular person's faith IS) rational.
There are a number of things we can't explain in scientific terms, as you put it, which a lot of very brilliant people put weight to. There are also things which ARE explainable by scientific terms that many brilliant people don't put any stock into at all--I was at a lecture by a Nobel Laureate of chemistry, who quite clearly didn't believe in global warming at all. Of course he stopped short of talking about it in the lecture so as to avoid being all controversial, but his implications were quite thinly veiled and it was quite obvious to anybody who had met him (had lunch with him).
When you said "religious belief is by definition irrational. You can't have faith without doubt." I am assuming you meant can't have faith WITH doubt--otherwise it means nothing because you can't have rational thought without some doubt either and you have not clearly differentiated between them on those bounds. In any case, even if that was a typo it is still nonsensical and untenable--there is no prerequisite to faith that says you can't doubt.
Regardless, there is a mathematically impossibility in science--however advanced in this century or the next 10--being able to explain everything in the universe. To make decisions in that arena is not de facto irrational.