A tabaxi ranger/assassin in my game made a pact with an unknown power (homebrew deity-like undead necromancer from the Death Plane). To achieve this he became an undead tabaxi (and he took one level in warlock). So now he is a creature that's both humanoid and undead.
Party composition (level 10): paladin, eldritch knight/wizard, ranger/assassin/warlock, rogue, warlock.
What are the mechanical consequences, both in terms of benefits and penalties, that arise for a PC with both humanoid and undead creature types?
The most prominent issue is healing.
The majority of healing spells (among them the most frequent ones, Healing Word and Cure Wounds) don't affect the undead. There are still some ways to heal yourself (see this question for ways of healing the undead), but it's "harder" to heal you. Most, if not all, healing spells that rule out undead creatures use the following wording:
Your paladin's Lay on Hands won't work on you either, for the same reason.
I think it's safe to assume that the mixed-type player character is affected by the restriction.
The best guideline we have on the topic is the Unearthed Arcana article that introduces Centaurs and Minotaurs as playable races. Those two races have the following trait:
OP's homebrew player race is a mix of humanoid and undead (however that works), but the principle is the same. Note that Unearthed Arcana is only beta-test material, so this is not RAW, and the trait might change if the races are ever released (if they even keep their hybrid nature at all).
Furthermore, the restriction on healing undead specifically rules them out - it doesn't state "this spell works only works on creatures that have a type other than undead or construct". In that case, you could probably affect mixed-type creatures, but the current version is unambiguous in my opinion.
Other issues include clashes with Cleric and Paladin abilities
Most prominently, you would be affected every time a Cleric or Paladin in your vicinity use Channel Divinity for e.g. Turn Undead. That won't be as much of an issue since your party doesn't have a Cleric, but you might still be accompanied by a Cleric NPC, or a player that later joins your group might want to pick one. Also, you do have a Paladin - and while they don't have access to Turn Undead, depending on their subclass, they might have Turn the Unholy, which will affect you as well.