With the help of @elliothartley and Amit Agarwal's Add Javascript Code in Blogger Posts post, we worked out a way to add a Mapbiquity web map to a Blogger post. You basically have to force Blogger to accept a <script> tag. See Amit's post for the details. Presumably for security reasons, Blogger will not initially accept these tags.

You will also need to add a bit of styling to place the map above blogger's "click-blocker" and remove the styling blogger adds to images. We'll eventually add this to the Mapbiquity code base so it's seamless, but for now we'll just have to use this workaround. Below is the code to add to your blog. You will obviously need to replace the <script> tag below with the generated <script> tag from your Mapbiquity account.

<style>
#mapContainer img
{
   border-color: none !important;
   border-style: none !important;
   border-width: 0px !important;
   padding: 0px !important;
   margin: 0px !important;
}
</style>
<div style="height:400px;width:400px;">
   <div id="mapContainer" style="z-index:11"></div>
</div>
<script type="text/javascript" src="http://www.mapbiquity.com/MapScript/js?..."></script>