Measurement invariance for binary categorical data and continous together: are there any special considerations?

[Z L]

Hi, 

I have read in this group (also checked Wu and Estabrook, 2016) that when an observed variable has only one threshold (it is binary) we cannot distinguish threshold, loading and intercept for measurement invariance in multiple group comparisons. So we have to constraint everything at once and test scalar invariance and compare it to the baseline model. But here I wonder whether this applies for cases where there are binary data and continous. Specifically, I am trying to compare this path analysis model across groups:

So, I wonder whether I should consider some steps to account for the continous part of the model. Do you know? What is the correct approach for the cases when you have binary data and continous all in the same model.

Thanks!