Have you tied .psd instead?
Never used to have this issue before. Not sure if something changed during an update.
InDesign doesn't respect many blending modes on image import, so perhaps that's the problem. Make a flattened copy and place that.
what are the exact versions of InDesign, PhotoShop and your OS?
I'd save the image as PDF/X-4 out of PhotoShop and place that in InDesign.
I Photoshop you should always save Layer Comps (Window > Layer Comps) with the selected layers in your file. In InDesign you should select these Layer Comps with import options.
A problem with Photoshop is, that no form of transparency other than reduced opacity is imported to InDesign. But the composite form of any Layer Comps should be ok. Here is a disadvantage of Photoshop PDFs or PSDs compared to AI/PDF or INDD/PDF imports in InDesign. I did a feature request, but this was withdrawn, to align Photohop PDF transparency with the counterpart of other Adobe programs.