Isabelle Lightwood is the first Shadowhunter we meet, following her through the Pandemonium Club before we're sure who—or what—she really is. She's first described as "beautiful, for a human—long hair nearly the precise color of black ink, charcoaled eyes" (1.13). We soon learn that she's a little more than human, she wields a whip almost as expertly as Michelle Pfeiffer in Batman Returns, and she's a terrible, terrible cook.
When Clary first meets her, she's kind of a witchy-B, looking down on Clary because she thinks she's a mundie. The only reason Clary has to dislike Isabelle seems to be that she thinks Isabelle is prettier than she is. Somehow, they manage to overcome these incredible differences and almost treat each other like friends. Isabelle even uses her fashion expertise to give Clary a mah-velous makeover.
And then there's Simon. He comes along and comes between them. Jace often tries to tell Clary that Isabelle is going to chew up Simon and spit him out. Like when he says, "Isabelle will cut out his heart and walk all over it in high-heeled boots" (9.44).
This is odd for a couple of reasons. We'd think that if he's so jealous, he'd want to convince Clary that she's going to lose Simon forever to Isabelle. Also, we want to say for the record that we never see any evidence of her alleged man-eating ways. Only rumors. The bad cooking, on the other hand. We're not going near that mess.
Now on to Alec Lightwood. Isabelle cares a lot for her brother Alec, who also lives in the Institute. To Clary, the two older Lightwood siblings look remarkable alike: "[Clary] could see exactly how much Alec looked like his sister" (5.118). What Clary doesn't immediately recognize is that Alec also has similar taste in guys.
Alec has a huge crush on Jace. Who wouldn't? Muscular, witty, and blonde? Dude has it all. Alec dotes on him, defends him, helps him get ready for battle by tattooing his bare, muscular arms, inking "every inch of bare skin […] with swirling patterns" (18.145)…
Wait, where were we? Oh, that's right, Alec's crush on Jace. It's a little unhealthy: "There was a kinetic, almost feverish energy to [Alec] that hadn't been there before. Something about Jace sharpened him, brought him into focus" (11.28). It's almost like he needs Jace to survive.
Nothing good comes of this crush. It leads Alec and Clary to have a petty fight out of jealousy, and it almost causes his death when he resorts to recklessly heroic behavior to try and impress Jace.
First, the fight. After returning from the near-suicide rescue mission to save Simon from the vampires of the Hotel Dumort, Alec confronts Clary for putting Jace's life in danger: "He left me behind! […] Normally I'd be with him, covering him, watching his back" (16.36). They argue for a bit, and Clary taunts him with the fact that he's never killed a demon, and that he should "admit this tantrum is just because you're in love with [Jace]" (16.46).
Ouch. Alec's having a hard time with his sexuality because his parents won't approve. Isabelle tells Clary to keep it a secret. To her credit, she does, even if she does use it to slap Alec in the face.
Clary's never-killed-a-demon insult and Jace's subsequently saying, "I like anyone killing things" (18.155) prompt Alec to put his life in danger during the fight with Abbadon in the name of impressing Jace. All it does is get Alec put in the nursing ward.
Things do work out in the end, though, as Magnus Bane nurses Alec back to health. Clary and Alec kiss and make up in the end (not literally, of course), but only because Alec found another man and doesn't feel like Clary's his competition any longer.
We don't see the Lightwood parents, Maryse Lightwood nee Trueblood, and Robert, or Max, the youngest Lightwood, in City of Bones, but we hear about them, and we hear nothing good. The parents are not only alleged homophobes, but they also played a large part in Valentine's Circle, determined to wipe out all Downworlders for the sake of bloodline purity. Maybe they just hate everyone different than them. Lovely. We can't wait to meet them.