  We present an extensive analysis of a model in which the (Majorana) Dark
Matter candidate is a mixture between a SU(2) singlet and two SU(2) doublets.
This kind of setup takes the name of singlet-doublet model. We will investigate
in detail an extension of this model in which the Dark Matter sector
interactions with a 2-doublet Higgs sector enforcing the complementarity
between Dark Matter phenomenology and searches of extra Higgs bosons.
