Are tumor-associated antigens found only on the membrane of cancerous cells or just over-expressed on the membrane of carcinogenic cells?
In other words, are these antigens also found on healthy cells?
I'll answer a slightly different interpretation of the question, which is whether the proteins (epitopes, actually) that are presented by cancer cells are neoantigens (varieties of proteins that only occur in the cancer cell due to mutations) vs 'wild type' antigens that can be found in other non-cancerous cells, but are over-expressed (or improperly expressed) in the cancer cell.
For melanoma, some of the potentially most useful immune-system targets are 'normal' proteins that are over expressed in cancer cells and rarely expressed in non-cancer cells. These include cancer testis antigens, which are proteins normally mainly expressed in germ line cells, but are accidentally expressed on cancer cells and lead to these cells being targeted by t-cells. See (for instance) the paper Cancer testis antigen and immunotherapy, ImmunoTargets and therapy (2013), pp. 11-19. For non-small cell lung cancer, Analysis of GAGE, NY-ESO-1 and SP17 cancer/testis antigen expression in early stage non-small cell lung carcinoma.
Carcinogenic tumor associated antigens correspond to any peptide chain (antigen) which triggers an immune response from the host. This means that they can be found anywhere inside, at the membrane, and outside of the cell: inside the cell (intracellular), at the cellular membrane and exposed to the extracellular environment, or even secreted.
Depending on the oncogene, they can be also eventually be over-expressed (anywhere there are supposed to be, including the membrane of cells).