Do the images show correctly in the front-end article when it is saved?

The problem is caused by the following css rule on line 56 of your template's template.css file, in particular the display:block style.

img {
    display: block;
    max-width: 100%;
    height: auto;
}

Go to Extensions -> Templates, and click on the name of your template to edit it. Click on the Template Options button, then on Custom Code. In the Custom CSS field, add

img {
    display: inline-block;
}

Save.