Are you talking about hull integrity, or wear and tear?
Hull integrity doesn't directly affect the health of you modules. However, the more damaged you are (as in the lower your hull % is), the higher the chance a weapon will breach the hull and hit a module. You may have noticed that weapons usually have their breach chance listed as "X% - Y%". The enemy's breach chance starts at the lower number when you're at full health, and move towards the higher number the more damaged you are. Because of this, a stronger hull kind of helps with module life, as it takes more damage to wear you hull down, thus it takes longer for your enemy to start getting the higher breach chances.
Wear and tear integrity affects your hull integrity. At 0% wear and tear, your hull can take your listed hull integrity's worth of damage (after resistances) before failing. At 100% wear and tear, it will only take 70% of your listed hull integrity's worth of damage before your hull fails. Your hull will still be listed as fully repaired, but at 100% wear and tear you're effectively at 70% hull.