# interpreting interaction terms in non linear regression

I have a hard time interpreting my coefficients in my nonlinear regression. In particular, I have a negative binomial, with two dummy variables: Treatment and (being) foreigner, outcomes are count data.

In my first estimation, I have

     Variables |   Coef.     P>|z|
Treatment |   -0.05     0.896
Foreigner |   -0.7     .0.035


So the treatment does not seem to have an impact and foreigner is significant.

In my second estimation, I have an interaction terms and thing dramatically changes. The AIC and BIC improves a lot.

            Variables |   Coef.     P>|z|
Treatment |   -0.9       0.04
Foreigner |   -1.8     0.001
Treatment Foreigner  |   2       0.001


But how should interpret the effects? Is there a way of understand the general effect of treatment (independent of the foreigner?)

If I understand correctly, the treatment effect for non-foreigner is exp(-0.9)-1= -0.59, that is 59% less than control non-foreigner , and the treatment effect for foreigner is exp(-0.9+2)-1= 2.00, which is 200% more than the control foreigner. Is that right?

It is puzzling to me because I do not expect the effects are completely different for foreigner and non-foreigner.

I appreciate any help with the interpretations. Thanks a lot!