This paper presents multiwavelength imaging and broad-band spectroscopy of the relativistic jets in the two nearby radio galaxies 3C 371 and PKS 2201+044, acquired with Chandra, HST, VLA, and Merlin. Radio polarization images are also available. The two sources stand out as intermediate between FRIs and FRIIs; their cores are classified as BL Lacs, although broad and narrow optical emission lines were detected at times. The multiwavelength images show jet morphologies with the X-ray emission peaking closer to the nucleus than the longer wavelengths. The jets are resolved at all wavelengths in a direction perpendicular to the jet axis. The jets SEDs are consistent with a single spectral component from radio to X-rays, interpreted as synchrotron emission. The SEDs show a progressive softening from the inner to the outer regions of the jet, indicating that the electron break energy moves to lower energies with distance from the core. Overall, the X-ray and multiwavelength properties of the jets of 3C 371 and PKS 2201+044 appear intermediate between those of FRIs and FRIIs.