  We extend the minimal supersymmetric standard model with bilinear R-parity
violation to include a pair of Higgs triplet superfields. The neutral
components of the Higgs triplets develop small vacuum expectation values (VEVs)
quadratic in the bilinear R-parity breaking parameters. In this scheme the
atmospheric neutrino mass scale arises from bilinear R-parity breaking while
for reasonable values of parameters the solar neutrino mass scale is generated
from the small Higgs triplet VEVs. We calculate neutrino masses and mixing
angles in this model and show how the model can be tested at future colliders.
The branching ratios of the doubly charged triplet decays are related to the
solar neutrino angle via a simple formula.
