The first impression that we get of her is that she is a stiff, cold, strict, unforgiving woman who is miserable and power-hungry. It's not too flattering. Even her physical description, as frail, with a face swallowing her nose, and even slightly crippled, isn't one that lends itself well to positive appraisal. If you are capable of looking beyond all of the surface descriptions, it is easy to pity her. Offred describes her lonely little life with only her garden as a companion, and her childless existence: it sounds pretty miserable. And several times throughout the novel, Offred herself pities Serena her position; imagine having to go through that incredibly uncomfortable ritual in the hopes of having a child. It would be awful. So, she is painted as mean and selfish, but it's hard not to at least be slightly sympathetic towards her because of her situation.
Our impression starts to change a bit when she approaches Offred about possibly using Nick as a means to get pregnant. She displays a bit of flexibility with the rules, and the willingness to be a co-conspirator in rebellion. She softens a bit. All of a sudden, she is a team-player with Offred. We realize that she too is willing to bend the rules and work around the restricting system they live under.
Overall, she is a rather unlikable character, but one that elicits at the least pity, and at the most sympathy. I hope that helped; good luck!
I almost see her as a very lonly individual. Becuase of the way their society works, she no longer feels that she is loved or wanted by her husband. We can see this through the jelousy that Offred speaks of (Offred doesn't really say anything about jealousy, but we can see that Serena is or may be jealous through what Offred does say as well as through Serena's actions and words) when Serena, Offred, and the commander are in the bedroom and the commander is doing his duty of filling Offred with his sperm to impregnate her. We can see the only reason Serena has any involvement in this scene is becuase she has too. Her actions after the commander leaves the room clearly express jealousy which is likely do to the fact that she feels lonly. The scene where she sets Offred up with Nick can also be seen as an expression of jealousy and lonlieness. She sends Offred to sleep with Nick not only to increase the chance of Offred getting pregnant, but also as a way to get Offred out of the house and away from Serena's husband becuase of the fact that she is jealous and lonly. Here jealousy is again expressed at the end of the novel when she finds the top with the purple sequins on it and the cloak that the commander bought for Offred to take her to the brothel.