Likelihood for regression problem in which the response is continous and zero-inflated, mixtures? any examples?

PyMC offers both Zero-Inflated Poissonand Zero-Inflated Negative Binomial distributions. But if you need a truly continuous variable, then you can take a look at examples of mixtures such as this for some ideas. Or if you have something started, you can post and see if others can get you headed in the right direction.