The iframe will render in the same mode as the containing page, regardless of any meta tags, or doctype settings. I also noticed mixed results when the doc or browser mode is manually changed using the dev tools, so don't rely on that. If you want to be super safe, load a new browser tab whenever you change the doc mode - I don't trust it!
This quick page I did up will give you the compatibilty information you're after: http://stevesspace.com/test/quirks/modern.html
<!doctype html>
<html>
<head>
<meta http-equiv="X-UA-Compatible" content="IE=9" />
<title>Inner page</title>
<style>
.pass
{
color: green;
}
.fail
{
color: red;
font-weight: bold;
}
#quirks-mode
{
color: #fff;
color: f00;
}
#not-quirks-mode
{
color: green;
color: fff;
}
</style>
</head>
<body>
<div>Quirks Mode: <span id="quirks-mode">true</span><span id="not-quirks-mode">false</span></div>
<div>Javascript: <span id="scripts-enabled" class="fail">false</span></div>
<div>Array map support: <span id="array-map" class="fail">false</span></div>
<hr />
<div>Doc Mode: <span id="doc-mode"></span></div>
<div>Compat Mode: <span id="compat-mode"></span></div>
<hr />
<div>SVG Circle should render below</div>
<svg>
<circle cx="50" cy="50" r="50" style="fill: green;"/>
</svg>
</body>
<script type="text/javascript">
document.getElementById('doc-mode').innerHTML += document.documentMode;
document.getElementById('compat-mode').innerHTML += document.compatMode;
document.getElementById('scripts-enabled').innerHTML = 'true';
document.getElementById('scripts-enabled').className = 'pass';
if (Array.prototype.map) {
document.getElementById('array-map').innerHTML = 'true';
document.getElementById('array-map').className = 'pass';
}
</script>
</html>