The second book of the Gray Death trilogy, Mercenary's Star, is set on a Combine-occupied Lyran planet. The Combine are the antagonists, but there's some stuff here for a fan.
There's the Wolf's Dragoons story arc that is (naturally) linked with House Kurita, chronicling the feud between the two and Theodore's eventual rise to Coordinatorship. The second book is nearly all Combine, the others divide the narrative roughly half-and-half. The first is the best, the two others OK.
Wolves on the Border
Heir to the Dragon
Then there's the "Camancho's Caballeros" trilogy that tells the story of a mercenary regiment that gets hired by Theodore Kurita's cousin, "Uncle Chandy" aka Chandrasekhar Kurita. All books involve the conspiracy of Black Dragon Society to overthrow Theodore or at least overturn his too liberal policies. While written from POV of the regiment, there's plenty of detailing the customs and environments of the Combine and plenty of political intrigue. In fact, 'Mech battles are few and far between here. I liked these a lot, I would say that at times I almost thought I was reading a "real" novel and not just BT books. Highly recommended, not just for Combine fans.
Hearts of Chaos
There's also two books describing the Combine-Ghost Bear war that was engineered by the Black Dragon Society. They are mostly from the Clans' POV (especially the latter, from Ghost Bear POV; the former is from Nova Cat POV) but still provide some insights into the Combine.
Path of Glory
Test of Vengeance
Far Country is simply wrong on so many levels, and while all the characters are from Combine, it's not worth your while unless you're on a mission to read through every BT book ever.