You just see there are transmembrane proteins which go from one surface to other surface and integral proteins one the out side of both surface.
So Int. Protein – Phospholipid – Phospholipid – Int. protein (PLLP)

also there are some sugars that form the glycocalix on the outside.

ok, so here is what the book means by " the protein molecules may be on the inner membrane surface, on the outer membrane surface, or may extend entirely through both membrane surfaces".
There are two types of membrane proteins: peripheral and transmembrane. Transmembrane proteins are the ones that can easly be seen in asutoshsahu’s picture. They span the whole membrane.
Peripheral proteins, on the other hand, do not span the whole plasma membrane, but in stead they are attached to one of the two sides: either interior or exterior.
What your teacher said is kinda true, but not exactly accurate. the lipids and proteins form a complex structure, they are not stacked like a sandwich. More than 50 years ago two researchers, named Davidson and Danielli proposed a model for the cell membrane that was kinda like a sandwich: protein-lipids-protein. This model was proved to be inaccurate and replaced with the fluid mosaic model in subsequent years.

Hope i cleared it up a little bit

Yes, these are Intrinsic and Extrinsic proteins…. Covers 50% of surface area of cell membrane and useful for passive and active transport…

The inner membrane of the nuclear envelope is connected to the outer nuclear envelope membrane through nuclear pores. It contains a number of proteins involved in the structural organization of the nucleus and the attachment of chromatin to the nuclear envelope. In metazoan cells, the inner nuclear membrane contains proteins of the nuclear lamina, a protein meshwork underlying the nuclear envelope and providing structural support. Mutations in inner nuclear envelope proteins can cause nuclear envelopathies, a number of genetic disorders in humans.

glycerol is on the outside and the fatty acid tail is on the inside

the reason is because the fatty acidis soluble in water but the glycerol doesn’t dissolve
that is why there are inner membrane proteins to check and allow whatever the cell needs (its is one of the reason it is called a semi permiable membrane)

While the plant cell has a rigid cell wall, an animal cell membrane is a flexible lipid bilayer. The lipid molecules (mostly phospholipids) that make up the membrane have a polar, hydrophilic head and two hydrophobic hydrocarbon tails. When the lipids are immersed in an aqueous solution the lipids spontaneously bury the tails together and leave the hydrophilic heads exposed. Thus this is a handy membrane to use, because it can automatically fix itself when torn. There are three different major classes of lipid molecules – phospholipids, cholesterol, and glycolipids. Different membranes have different ratios of the three lipids.

you’re little bit confused, aren’t you?