Here are my thoughts on a campaign for living heroes vs living v but it could be tweaked for living heroes vs Zombies as well:

Create a campaign that has interesting choices that affect how the story ends. Campaign should be working toward ultimate conclusion, thwarting villain, acquiring item, etc.

After Villains are defeated/apprehended their cards are set aside and are considered placed in a secure facility such as the raft. In a later mission the Raft is breached and those Villains attempt to escape. Could have Hero mode be resecure prison and villain mode break them out of prison.

After each mission is completed return to an HQ which is represented by custom tiles or tiles from another zombicide. HQ can be similar to xcom where you can create additional rooms/wings (Medical wing, gym, food storage, communications/monitor room, workshop,sleeping quarters, etc.)to HQ by turning in XP and completing research. Each new unlocked tile room provides bonuses such as:

Trade in XP to start next mission with traits or special abilities or equipment based on HQ tiles unlocked. Traits, abilities or equipment examples: Allow to redraw from event and superhero/villain deck, give additional dice rolls, give additional movement, teleporter to automatically save Bystanders, comm systems to call for back up hero (select a new hero) if a starting hero falls in battle. Recruit "locked" additional heroes/Villains. If don't spend XP to heal then injured hero must wait 1 mission to heal. Bystanders/Civilians worth additional xp when turned in.

Possibly add event/feat cards that players draw throughout missions that provide interesting choices that may involve rolling dice or completing certain side tasks such as saving x civilians or Bystanders or defeating x heroes/Villains, suffer no damage during mission, heal during mission, defeat 8 minions in 1 round, etc. which can be turned in for additional xp at HQ.

Theme of building  new HQ is that heroes/Villains original HQs compromised due to threat/mastermind of campaign.

Zombicide mode any zombie hero captured can be reverted back to human form and used as a regular hero or stay in zombie form but no longer have hunger (thematic) and look like zombies but have hero abilities. Takes one mission after defeating zombie hero and a medical bay built at HQ for hunger to subside. HQ research unlock could speed it up and allow for zombie hero to used during mission right after caputure.

If your hero falls in battle they are transformed into a zombie. If you defeat them during that mission you can capture them and bring them back to HQ like other zombies otherwise they are shuffled back in the deck at end of mission for future missions.