Bring element to front using CSS

Solution 1:

Add z-index:-1 and position:relative to .content

#header {
    background: url(http://placehold.it/420x160) center top no-repeat;
}
#header-inner {
    background: url(http://placekitten.com/150/200) right top no-repeat;
}
.logo-class {
    height: 128px;
}
.content {
    margin-left: auto;
    margin-right: auto;
    table-layout: fixed;
    border-collapse: collapse;
    z-index: -1;
    position:relative;
}
.td-main {
    text-align: center;
    padding: 80px 10px 80px 10px;
    border: 1px solid #A02422;
    background: #ABABAB;
}
<body>
    <div id="header">
        <div id="header-inner">
            <table class="content">
                <col width="400px" />
                <tr>
                    <td>
                        <table class="content">
                            <col width="400px" />
                            <tr>
                                <td>
                                    <div class="logo-class"></div>
                                </td>
                            </tr>
                            <tr>
                                <td id="menu"></td>
                            </tr>
                        </table>
                        <table class="content">
                            <col width="120px" />
                            <col width="160px" />
                            <col width="120px" />
                            <tr>
                                <td class="td-main">text</td>
                                <td class="td-main">text</td>
                                <td class="td-main">text</td>
                            </tr>
                        </table>
                    </td>
                </tr>
            </table>
        </div>
        <!-- header-inner -->
    </div>
    <!-- header -->
</body>

Solution 2:

Note: z-index only works on positioned elements (position:absolute, position:relative, or position:fixed). Use one of those.