Can We Inherit Neurosis?

Yes. But let me explain.   
First neurosis results from the impact or introduction of adverse events very early in our lives. So a mother smoking and taking drugs, a birth with far too much anesthetic, an infancy of lack of touch and indifference, a mother who goes to work and therefore cannot nurse and cannot love the child, etc... The ramifications are endless. But the brain and body do not forget.  It produces methyl to mark the spot and informs us of the force of the pain.  But that is not the end of the story: methyl can be inherited, inherited methylation which mingles with methylation from trauma to disrupt normalcy.  That is, a neurotic parent can inculcate adverse chemicals to change the trajectory of the child. In that sense it is inherited; it joins with imprinted pain to add to the load that must be absorbed and integrated.
In other words, trauma alone may not be enough to produce a full- blown neurosis, but parental legacy might put us over the top into neurosis. Those parents, also loaded with pain, may spill some of the load onto the baby; this adumbrates to foreshadow a danger ahead. This inheritance research is the work of BioMedical Research by Rudolph Jaenisch of MIT and can be found here. I assume that this has an effect on the genes where inheritance seeps into the newborn. 
I believe that with a normal parental configuration and with a loving life, one can avoid a deleterious neurosis.  Not completely, but enough not to be mentally ill.   But failing healthy parents, one cannot.  Believe it or not, they call it parental imprinting.  And it is imprinted and becomes part of  us.   
Methylation affects and alters gene expression and eventually distorts us, our behavior, and our neurochemistry. This results from when the egg and sperm are fertilized and  then shipped to the offspring.  Inside that shipment is a whole history of the parents, and the history contains fragments of the pain from the grandparents, as well.  This all happens so early and with such an impact that serious disease might result, including cancer.   
We need much research in this area but inheritance counts, not in the booga-booga sense, but in science.