LR does fine with jpg's and other formats, though it doesn't read .bmp, .trg or some other weird ones.
It is true that LR will only import one file of a specific filename. It seems to take .psd's first, then .dng, then .nef, then .jpg. As soon as it finds one, it ignores the rest. Unfortunately, it does this silently, not informing or warning you that some images haven't been imported.
Why are you shooting raw+jpg, anyway? With a product like LR, I don't see a reason for it. It just takes more space and clutters up the folders. The raw files display just as quickly and are just as usable.