What type of singularities is your model having problems with? Is the sofware giving you and error telling you that your model is insuficiently constraint ? Sometimes this error occurs if model have a very large discrpancy in stiffness between materials. This is bacause the stiffness matrix is ill condition.
Is the problem you refering about stress discountinueties between the two materials at the join? If that is the case this is not necessary a singularity but a physical manisfestation of the fact that the model has two or more materials sharing the same face. How much difference there is between the to poissons ratios of the materials? Did you run a multy pass adaptive (MPA) and make sure you it was a singularity ? Could tell me a little more about the problem may be I can help.