"Le riz et les pâtes"
You haven't answered the question, but only reinforced TFles point. If we go by your analogy: in English you'd say "can I have some rice?" or "can I have some pasta", not "rices" or "pastas", so there is NO discrepancy between them.
In French there IS a discrepancy because with one you use the singular article 'le' and with the other you use the plural 'les'.
Because in English we do not say "the pastas". Though we do say "the pastries". You can never translate into another language word-for-word as a lot of the times, it will make no sense. Part of what you are learning is how to use words, not just what they mean. Your intuition was right on!