Seems like you can get it to work in IE if you assign position: relative to the paragraph, but I can't get it to work in Firefox:
table.test {
background-color: white;
color: black;
opacity: .5;
filter: alpha(opacity=50);
}
table.test p {
background-color: white;
position: relative;
opacity: 1;
filter: alpha(opacity=100);
z-index: 3;
}