Seeing Wikipedia, morphemes refer to minimum components of words. Even "-ed" which makes past tenses is called morphemes according to some sites.
So I'm afraid that this is contrary to what the person wanted to know.

Some people may see 食べている as a single word. I can agree with that. When it comes to whether or not we can extrapolate it into 待たされていました, that will be a challenging question lol.
Frankly speaking, we have seen the words numerous times throughout our lives so we never try to break it down and analyze it to interpret the phrase. It's just automatic.

But I know the reason why the person asked the question. In English it is clear that 食べている is consisted by several words: "be eating" and we can easily detect that there is a present continuous tense.
In Japanese it seems more integrated as if it were a single word.

In conclusion, I think this analytic way of thinking grammer is unique to English native speakers.
Most Japanese native speakers have never spend their time analyzing grammatical structures in Japanese sentences. This is some kind of cultural differences.