This is what I've used before to display pdf's and it has never asked me to download in Chrome or IE.(I answered with this on a different question so you know)
I have personally used the Content Editor Web Part (Located under Media and Content) to display various documents within the page (no need to have the page be opened on an entirely different page) maybe this is what you would want?
To do this, add the Content Editor on your page. Select "Edit Web Part" then click on the text that appears on the web part ("Click here to add new content").
At this point it should look like you are about to type in a text box. Now click "Edit Source" on the Format Text ribbon. This will edit the HTML within the Content Editor itself instead of the entirety of the page.
Now insert this code:
<object><embed width="850" height="850" src="..." type="application/pdf"></object>
As you can see there is a src"..." where the ellipses are put the link to your document or image or whatever that you have stored within your SP site. (this might take some playing with the link). This case also is for a pdf and you might need to change that application/pdf - might work with any document type however.