I wonder if you were speaking generally here, or if you were referring specifically to the Chemical Imbalance theory of depression/anxiety.
Often espoused by the marketing departments of Big Pharma, and by now firmly lodged in the public consciousness, the idea that abnormal monoamine levels (e.g. serotonin, noradrenaline) in the brain causes depression, is (to say the least) highly controversial. Some might even call it "debunked". Or, more charitably perhaps, just a highly persistent meme that's never really had much to do with science from the get-go.
BTW, I say this as someone who saw successful results using SSRIs (Citalopram) as a treatment for depression some years ago. Given that the relationship between serotonin and depression seems subtle, indirect, and poorly understood at best, I don't pretend to be able to explain why SSRI treatment "worked" for me! Placebo? Coincidence? Genuine effect which empirically exists but we do not yet understand the mechanism (a bit like lithium)?
But the strange fact is that SSRI therapy does seem to help with depression in many people, just as lithium seems to help with mood even though we don't completely understand why.
With the example of serotonin, even though the SSRI effects serotonin levels almost immediately, it can take several weeks for depressive symptoms to improve. Therefore it is unlikely that inhibiting serotonin transport alone accounts for the anti-depressive effect. It has more recently been theorised that the strong anti-inflammatory effect of SSRIs may be involved, as depression is increasingly known to be related to chronic inflammation.
Lastly I'm pretty skeptical about "imbalances" altogether (though I took it for granted at the time). For example, when I and others have been prescribed SSRIs, there have generally been no medical tests given first which might detect or confirm any such imbalance. In fact I'm not even sure such a test is possible. Instead, they give the pills out solely on the basis of a personal report from the patient, which the physician interprets to indicate depression.
Sure, they are heavily interrelated. They are vastly different models of the same thing. While we can understand some processes simply by chemistry, we don't get too far with that when trying to understand social behavior. On the other hand psychology can model processes and behaviors on another level. Sometimes they overlap well but far too seldom.
They will probably not converge well in our lifetime because we are really slow in understanding of complex interrelated systems and cannot make all the experiments we need to quickly advance scientifically.