Between these two texts, we don't know too much about Muriel. The best glimpse we get is through Seymour's diary in "Raise High the Roof Beam, Carpenters" when he characterizes their relationship via a few sketched vignettes. What we see is that Muriel and Seymour are entirely different people. He is spiritual and socially detached, while she is down-to-earth and extroverted.
What's interesting is that Seymour fully understands what Muriel is like. He knows, for instance, that her interest in getting married has more to do with the institution of marriage than it does with her love for him. In his diary Seymour writes:
"She wants to get a very dark sun tan, and go up to the desk clerk in some very posh hotel and ask if her Husband has picked up the mail yet. She wants to shop for curtains. She wants to shop for maternity clothes. […] I have a feeling, too, that she wants her own Christmas tree ornaments to unbox annually, not her mother's. ("Roof Beam" 4.7)
We also get the sense from these diary entries that Muriel's reasons for choosing Seymour may be suspect. "She gets a vast satisfaction out of telling her friends that she's engaged to the Billy Black who was on 'It's a Wise Child' for years," he writes ("Roof Beam" 4.7). If Seymour's reasons for loving Muriel are based on childhood events (see Seymour's "Character Analysis,") then perhaps so are Muriel's. And possibly to her own detriment, as well: "On the whole," admits Seymour, "I don't make her really happy" ("Roof Beam" 4.7).
If you're interested in learning more about Muriel and her mother (Mrs. Fedder), we suggest a reading of "A Perfect Day for Bananafish."