You Can't Force Images and Text to Stay On The Same Page
The answer is: sometimes. Generally, the answer is really “no,” because unlike print formatting, eBook formatting does not have precise control over vertical and horizontal alignment. As we discuss in Text reflows--or wraps. and Is it true that readers can change how my book looks?, text in ebooks reflows. This means that when people resize the font, as the sample images in those articles show, the reflow of the text might move an image to the next screen. Or, it may move a caption for an image to a new screen.
For some things, like images with captions, we can use commands called “keep-togethers," but not every device honors this command. In fact, most don't honor the command. We put the commands in there, to "future-proof" the book, so that when the devices do honor the commands, the images and captions will stay together--but for now, the vast majority simply ignore it. Therefore, while we do the best we can, we can’t guarantee that certain things will stay together on every device, at every font size, and every font, available on the market.
As you can see in the linked articles, the text highlighted in purple (for the Prince and the Pauper examples) is on one page with the image when the font is smaller. When the user makes the font larger, the text becomes separated from the image on a new "page." This is the challenge of ebooks--they are constantly changed by the readers, using smaller and larger fonts, different-sized devices and in some cases, even different fonts.
Devices don't really "understand" the idea of two separate elements--an image and its caption--as being part of the whole. That's why the images and the text can "come apart." (This doesn't happen in Fixed Format, but that's a route you should take only if absolutely required. You can read about Fixed-Format eBooks in the eBook Productions section by clicking that link, if you think you need that layout option.)
It's important to embrace the concept of "reflowing text" as you embark on your digital publishing journey, as this will save you a lot of aggravation and stress.