Question: So I'm creating my first D&D 5e campaign and I want there to be an even balance between combat and non-combat with a slight bias to the non-combat style of missions. However I'm unsure about how to deal out XP for these situations and how much is a suitable amount. Also should I some characters get more XP than others for certain missions? For instance if you're trying to steal an artifact from a temple then a rogue will be very good at this while a barbarian will likely not be able to do much and so deserves less XP than the rogue but is this a fair way of managing things?

Answer: 
You can also award XP based on how important the non combat event was toward progressing the general adventure. A technique I have found to work fairly well is to take the party's average level as a base CR. Tiny inconsequential events (ex: talking to a shopkeeper in character) are worth CR minus 2 as an experience award. Moderate events (ex: finding an important clue, or procuring a map of the area to be adventured in) are worth CR minus 1, while events upon which the adventure hangs (ex: Tracking down the BBEG's lair, unmasking the Evil Prime Minister) are worth a full CR. Award experience per the CR values given in the Monster Manual and DMG.

Thus if the party has an average level of 4, then finding an important clue has a CR of (4-1) or CR 3, and is worth 700 xp. If the characters were 3rd level, it would be worth 450 xp.

The nice thing about this is that tying the CR for the event to the party's level will tend to scale it with the characters, so that they never lose the incentive to find non-combat solutions, or to forgo non-violent interactions with the environment. Note that my values work for my campaign. Adjust and season for taste.

One last thing, if you do adopt an approach that rewards non-combat interaction, make sure the players are aware that you are doing so. If you don't tell them, they have no incentive to try alternative behaviors.
I play RoleMaster but the idea of XP is similar. 

The answer is in the word. I give experience points for relevant **experiences**. I dole them out (in order) by:

1. **Milestones**: Accomplishing a mission or reaching a certain plateau
2. **New experiences**: first time ever in town, picking a lock, meeting an owlbear, etc. (2nd time in a town, not such a big deal),
3. **roleplaying**: more on that later,
4. **Hits taken or received** (relative to monster difficulty),
5. **Spells** successfully thrown (relative to caster's level),
6. **criticals** (RoleMaster is a critical heavy playing system),
7. **ideas/specials** ("It was my idea to trap the gelatinous cube in the giant
squirt gun."),
8. **kills**, and
9. **treasures** (treasures are their own reward, in my opinion, and players usually don't get any XP for gold and magic items).

Rearrange or add to the list based on what is important in your campaign.

I also, with each new level, give the players a blank "Experience Sheet" form which has areas for hits taken, given, spells, ideas, thing encountered, etc. It's their job to keep track of things they've done individually on these sheets and I collect them when I'm going to award XP. (It's funny what some of them will put down to wrangle extra XP sometimes!) When I really like the way a character is playing their character (i.e. a character sniveling in front of a noble, polishing his boots, acting as a decoy) I make sure that the player wrote it on their sheet or I write it on a master sheet I keep for just those occasions.

Because I place the group activities highest (just watching an Owlbear rip apart your fighter is an experience), the individual experience is fairly well grouped with the more immersed individuals ending up getting a little bit more.

Hope this helped.