Basically the li is having a solid colour applied to it, and is being restricted to 10px high. One way to approach this is to make the li taller than the a tag and the text and then change the solid colour for a gradient (e.g. background: linear-gradient(to bottom, #ffffff 0%,#ffffff 97%,#f7fbf7 97%);) which fills it with white for the first 97% of the height, and then green for the last 3%.
You will need to do similar for the hover state/active page but with a bit of playing around you should be able to get this to work without changing the order of code or any other CSS.