Analyses when IVs highly correlated - is there anything I can do? I'm doing some analyses in which I have 1 continuous independent variable (IV) and 1 dichotomous independent variable (IV2) that's a demographic covariate. I'm now realizing that they are extremely correlated (~ .9). See image below.

Now what I'm wondering is there anything I can do (maybe some sort of centering strategy?) that will allow me to use both variables in my analyses? I was hoping to look at their interaction.
 A: I'll go out on a limb here.
I don't think looking at the interaction is useful here. As in: any interpretation of the interaction between the two predictors will be deeply mistaken.
You can interpret the effect of IV1 in the range 0-50, where IV2 will typically be 0. Any IV2=1 with IV1 in this range is an extremely abnormal observation, simply because this combination is unheard of. And vice versa. Therefore, it simply makes no sense to discuss things like "if IV2=0, then IV1 has an effect of $x$, while if IV2=1, then IV1 has an effect of $y$" or similar.
I like to recommend Miller & Chapman, "Misunderstanding Analysis of Covariance" (2001), who have a number of very enlightening examples and explanations.
What I would instead do is to include IV1 only, but account for potential nonlinearities, e.g., using splines. Then you can discuss the relationship between IV1 and the DV over different ranges of IV1 and note what the typical value of IV2 is over these ranges.
A: I agree with @Stephen that the interaction is unlikely to be useful.
If you really think that the effect of IV1 will be different at different levels of IV2 (which is what an interaction tests) then you could stratify: That is, do separate regressions for the two levels of IV2. You can then compare the results (although you won't have estimates of the size of the interaction). 
Since your DV is ordinal, you should probably use ordinal logistic regression, at least as a starting point. 
