  We present a multi-wavelength analysis of high-resolution observations of the
quadruple lens B1608+656 from the HST archive, acquired with WFPC2 through
filters F606W (V-band) and F814W (I-band), and with NIC1 in filter F160W
(H-band).
  In the three bands, the observations show extended emission from the four
images of the source in a ring-like configuration that surrounds the two,
resolved, lensing galaxies. B1608+656 was discovered as a double-lobed radio
source, and later identified as a post-starburst galaxy in the optical. Based
on photometry and optical spectroscopy we estimate that the stellar population
of the source has an age of $\sim$ 500 Myr. This provides a model for the
spectrum of the source that extends over spectral regions where no observations
are available, and is used to generate Tiny Tim PSFs for the filters.
Deconvolutions performed with the Lucy-Richardson method are presented, and the
limitations of these restorations is discussed. V$-$I and I$-$H color maps show
evidence of extinction by dust associated with one of the lensing galaxies, a
late type galaxy presumably disrupted after its close encounter with the other
lens, an elliptical galaxy. The extinction affects the two lens galaxies and
two of the four multiple images. The diagnostic of wavelength-dependent effects
in the images shows that corrections for contamination with light from the
lenses, extinction, and PSF convolution need to be applied before using the
extended structure in the images as a constraint on lens models. We will
present the restoration of the images in a subsequent paper.
