In 1935 Hugh Davson and James Danielli suggested that the phospholipid bilayer is sandwiched between layers of globular proteins. Thad been evidence of the presence of proteins and since both membrane and proteins could act as barriers, the belief seemed plausible. This became known as the Davson-Danielli model.
However, the theory had several flaws. It remains unclear how proteins contain the flexible fluid, as they are generally stiff and can’t cope well with outside movement. Another problem was that the amount and/or type of membrane protein varied greatly between different cells.
In 1966, with the help of freeze fracturing: the splitting of cell membranes between the two lipid layers and thus revealing a 3D view of the surface texture, the model was disproved as it displayed that the proteins were actually embedded inside the layer and were amphipathic.
Thus came the creation of the Fluid mosaic model of Singer and Nicolson in 1975. With the help of fluorescent labelling, it became clear that the components of the membrane were able to move within its structure. Two different colored membranes were fused together and instead of maintaining the same colors, they diffused into each other and moved around.
Further details can be found in the following video: