the pixel in any one channel possesses either 8 bit or 16 bit data, end of story. Each file therefore is determined to be either in 8 bit or 16 bit, with a total data capability of either 24 bit or 48 bit in RGB, and 32 bit or 64 bit respectfully. The color image is made of channels in grayscale only, the independent value to each pixel applies, but the compilation of all three [RGB] or all four [CMYK] total the larger bit depth number. Please keep in mind that a color channel is specific to the channel it represents and is not dispensable without changing the content of the entire file - if you move or replace a color channel, it will and does affect the entire image. For example, if I have an RGB file and I throw the G channel in the trash, the file immediately becomes a two color image of cyan and yellow, the values represented by the mix of R & B in the additive process, if I remove the B channel the file is now just cyan and magenta: These become compilation 16 bit files, but are still at just 8 bit per pixel information values, they are also known as multichannel color space (a .psd only format) and must be converted to either Duotone (eps, psd, or pdf formats only), RGB, or CMYK for output.
A raw capture can be one of many bit depths, 8 or 10 or 12 or 14, whatever, but this is determined by the combination of the camera's hardware, firmware, and software alliance; this is a manufacturer's design. Although you can create a 12 bit or 16 bit file, very little is done at this capacity due to the tremendous amounts of math involved. Photoshop CS now can apply more effects and tasks than any previous version when working in 16 bit, but even though it can, it still is cumbersome and much slower. 99% of all your color houses [Prepress], retouchers, printers, etc., work in 8 bit to color correct, enhance, or modify any file - resampling [interpolation] is probably the primary assignment for 16 bit data - and all printing devices are default to 8 bit.
Tiff is a lossless format with an independent directory capability far superior to most [all] file formats - it virtually is the best and most universal file format - this is why it is a larger file. Jpeg on the other hand actually has automatic limitations and with compression, file deterioration built in by degree of loss vs. size. Jpeg can be RGB or CMYK, but only 8 bit - 24 bit RGB & 32 bit CMYK. If you save a file in jpeg and compress it at say a Quality value of 7 with a Standard Baseline, the information of color is averaged in pixel sets or clusters of 4 square pixels, averaging some of the values out. Then if you save that same file again in jpeg at say Quality level 6 and Optimize the Baseline, you will make larger clusters or sets - still in groups of 4 pixels, just larger areas - averaging information, making the data content reduce in file size. This is also what causes tremendous artifacting and edge deterioration in contrasting pixel order.
Learn more about format and file information @ San Diego Smackdown, Feb 28-29