If your character does not get the full eight hours of sleep, then you don't gain the benefit of Natural Healing. However, that doesn't mean that you personally may be screwed, it just means you have to make use of a party staple to get what you need every night.
This spell is your ticket to full rest, and can be acquired relatively early into a Wizard's career, enables the party to not get ambushed due to a wide range, and allows you to get that full eight hours.
Having an elf in the party means you have a comfortable four hour period where the elf can keep watch while awake without losing any of their basic natural healing as well as being able to still recover any spells for the following day. Having two elves extends this to two shifts of 4 hours, which means all is well in the world of rest.
Five Person Shift rest
If you have five people, resting for a total of 10 hours, each taking a two hour watch shift from 10PM to 8AM, each person has a two hour watch and receives a full eight hours of sleep. If there's an encounter during the night that counts as a significant interruption, so you wouldn't get the benefit however.
There's reason to believe that a split sleep schedule is actually more natural; I'd certainly allow people to receive full resting benefits from such watch shifts.
Since Animal companions and familiars have scent and good ranks in the perception skills you could also use them to cover a shift if you taught them to keep watch and wake you up if they saw something via Handle Animal. Familiars and Animal companions are considered Magical Beasts so they do need their eight hours of sleep as well however.
What exactly counts as a "Significant Interruption"
With a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.
In the spell section of the players handbook it reads the following:
To prepare her daily spells, a wizard must first sleep for 8 hours. The wizard does not have to slumber for every minute of the time, but she must refrain from movement, combat, spellcasting, skill use, conversation, or any other fairly demanding physical or mental task during the rest period. If her rest is interrupted, each interruption adds 1 hour to the total amount of time she has to rest in order to clear her mind.
So that means that if you decide to use similar rules for natural healing, you can keep watch, but any of the above interruptions will cancel out the rest. (It's been suggested that sitting and listening is a demanding physical activity, but I'd ignore that if you're looking to make a house rule) If there's some kind of night combat then you have to add an hour onto the amount of time you have to rest to recover nightly ability damage and hit points.