Zombine

First Encounter

Zombines are first encountered in Half-Life 2: Episode One (chapter 3: Lowlife), when Gordon Freeman and Alyx Vance find a Combine troop train in the headcrab infested City 17 underground. Alyx coins the phrase "Zombine" in a joke merging the words "Zombie" and "Combine" together. The joke, however, falls on deaf ears: Gordon's ears. Another Zombine in the room ahead then suddenly gets up, pulls out a grenade, runs up to the door and kills himself allowing Gordon and Alyx to continue down the tunnel system where even more await. 

Other Encounters

Zombines continue to appear multiple times throughout the "Lowlife" chapter and several more times as Gordon and Alyx venture through the remnants of City 17. 
In Half-Life 2: Episode Two Zombines appear several times in the Antlion caves (chapter 2: This Vortal Coil) but mostly through zombie infested areas that appear afterwards in the following chapters.

Abilities

Zombines are slower than the traditional Headcrab zombie but are able to sprint for short distances. Like regular Headcrab zombies, Zombines will attack their targets with their claws but will on occasion, hold out a live grenade killing themselves and damaging everything around it (which will either result in hilarity or death, or in some cases both). The fact that they do this portrays either the fact that the Combine soldier is either to advanced for the Headcrab to control or Combine is simply attempting to end its miserable life as quickly as possible. This move can most easily be countered by using the Gravity Gun to pull the grenade out of the Zombine's hand and repel it back at them.
The combination of a standard Combine soldier armor and the fact that Headcrabs boosts their hosts endurance against damage, makes the Zombines very tough to kill.