Transmission of epigenetic regulation through surrogate mother
Epigenetic information is information that can be inherited through cell division that is not encoded in the DNA sequence. This includes, but is not limited to, DNA methylation and histone modifications (there is also non-chromatin based epigenetic information). A nice example is the centromere, the chromosomal region that binds the kinetochore and is important to attach chromosomes to the mitotic spindle during cell division. The location of the centromere on the chromosome is encoded by a specific nucleosome composition and does not seem to rely on the DNA that wraps around those nucleosomes: The DNA sequence at centromeres is not even conserved from chromosome to chromosome (with the exception of budding yeast), and there are several known examples of people and families where the centromere is in a different place. However, all the mechanisms for maintaining this epigenetic mark are encoded genetically. 

As epigenetic information is transmitted through cell division, it is directly inherited from the biological mother (with the exception of e.g. the centromere, most epigenetic marks from the father's chromosomes are removed when sperm is created). 

However, (some) epigenetic information can be modified. This is obviously important during development where gene expression patterns of a liver cell need to be stable but different from gene expression patterns of a neuron, even though both descend from the same cell. 

There is evidence that the metabolism of the mother will influence the epigenetic program of the child; diet being one of the determinants. It has also been suggested that epigenetic changes may influence behavior. Thus, it is indeed possible for the surrogate mother's epigenetic state to influence the epigenetic information of the children.