Clearly, from your description, the file is a bitmap eps (the kind that Photoshop creates, as opposed to a vector-based Illustrator EPS) However, it may be that what you're seeing when you place it in Illustrator and InDesign is the low-rez preview image, and not the full-resolution image itself. Double check what the size and resolution is in Photoshop. Depending on what the final usage is going to be, you might be able to get away with some up-sizing without too much pixelating.