Question

Why is it important that the phospholipid bilayer be both hydrophobic and hydrophilic?

Answer 1

It is important that the phospholipid bilayer is both hydrophobic in the surface and hydrophilic inside to control and manage the incoming organic compounds mainly water from exceeding the needed amount or destablizing the concentration established by the cells.
Hydrophilic is a characteristic of an object which is attracted to water or can synthesize with water. In contrast to hydrophobic like fats, oils and lipis which has a strong aversion and dislike to water molecules.
Transmembrane proteins are found in the plasma membrane. Hydrophilicregions are embedded within the membrane, and Hydrophobic regions project from both surfaces of the bilayer. 
Approximately 20-80% of the cell membrane is composed of lipids, the rest, is made up of protein. The lipid layer of the membrane gives it flexible and permeable characteristic. While the protein part assists in transport of molecules it needs to survive.