It depends what you mean by JPEG. Commonly, we're talking about JFIF/EXIF image file formats, which specify either one or three bytes per pixel (regardless of the colour space mapping those bytes to bits). Create a file that actually has only two discrete levels present, and it's no longer a JFIF/EXIF file. (And since throwing out high frequency information is the basis for JPEG compression, and all tonal changes in a bitonal image are by definition high frequency transitions, JPEG is a pessimal solution.)

For pure bitonal images using a JPEG-like compression, you'd need to be using JBIG or JBIG2, a format essentially for fax (and not commonly readable). A paletted solution that uses DEFLATE-style compression (redundancy mapping + Huffman or LZW-style bit reduction), such as PNG would be a better solution for most applications, however, since the position (and not merely the distribution) of the bits in the reconstructed image is guaranteed.