When you add it in to Construct, click on the SpriteFont, and look at the properties. Tweak these slightly (character width, etc).
Look at the h in your image above. It is picking up a line of pixels beside it. I assume it's a capital H, or maybe even a border.
I already explained that this is wrong.
It's not picking up pixels from other characters because the spritefont is upscaled from an original 1:1 scale bitmap image.
This is a glitch, not a SpriteFont configuration issue.
Do you mind if we see a capx or a sprite sheet?
Sure, here's a JPG copy of the original image:
<img src="https://copy.com/WT00FdgYYC4s/c2_spritefont_sheet.jpg" border="0" />
The sprite sheet image's resolution is 261x64px with each character having a 9x16px resolution, and the black background color is replaced with alpha transparency in Construct 2