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Hmm.. This is a brain tasking riddle even though I love to play games related to riddles. It helps to sharpen my brain and it improves my brain power and IQ.
After thinking about your question, the answer to your question is "WATERMELON" in my opinion. I will explain why I went for water melon.
Let's scrutinize the words and statements you provided for the question.
"There was a green house" => This means that the outer body of such thing should be green in colour. There are lots of fruits and materials with green outer segment (body) but the next statement gave me some clue to the answer.
"Inside the Green house, there was a white house" => I got to know that this is likely to be watermelon because I love eating the outer part of water melon due to some beneficial health benefits it posses. I do notice there is a white segment which comes before the green part. You can verify this by slicing your water melon and observe the white segment before the outer segment which is green.
"Inside the white house there was a red house" => Of course this will automatically lead you to the answer that this is water melon because this red portion is that part which we all love to eat. I will call it this nucleus of the watermelon. It is the most delicious part of the water melon.
"Inside the red house there were lots of babies"=> The babies mentioned here is known as the seeds of water melon. The seeds are always found inside the red portion of the water melon.
In conclusion, this describe a water melon without any doubt.
Thanks for reading and I hope this helps.