Morphemes are the smallest units of meaning in a language. Phonemes are the smallest units of sound in a language. In Chinese, each phoneme corresponds to a morpheme and each morpheme corresponds to a morpheme.
For example, in English we have the word "cat." "Cat" is a complete idea, and it cannot be broken down into smaller ideas based upon the word. "Cat" is also a complete sound. While each letter in "cat" corresponds to a specific sound, separately they are not complete. Every character in Chinese represents a single morpheme and has a corresponding phoneme very similar to the word "cat".
On the other hand, English has many cases where more than one phoneme is corresponds to a single morpheme. For instance, in telephone there are two morphemes: tele and phone. In the same word there are seven phonemes: t, e, l, e, f, o, and n.