Emma's mom has been in several relationships, looking for the right guy. At the time our story takes place she's married to Martin, who Emma can't quite warm up to: "I still can't hear Martin's name without rolling my eyes. My mom married him last summer, saying this time she found true love" (1.19). Yeah, Emma's a little cynical about her mom's love life as well as her own. For more on this, though, check out Emma's analysis elsewhere in this section.
Other than this, we don't know a whole lot about Emma's mom and Martin. They just aren't major players in this story. Instead, as is the case with teens all over the world, Emma spends a fair amount of time doing her own thing away from them.