Link inside a button not working in Firefox

I have two links inside a button but the links don't seem to work on Firefox.

<button class="btn login">
    <a href="/login"><b>Log In</b></a> 
          | 
<a href="/signup"><b>Sign Up</b></a>
</button>

I tried JavaScript onclick and redirecting - even that is not working.

This doesn't work because it is not allowed by HTML5:

Content model: Phrasing content, but there must be no interactive content descendant.

Interactive content means any of the following elements:

a audio (if the controls attribute is present) button details embed iframe img (if the usemap attribute is present) input (if the type attribute is not in the hidden state) keygen label menu (if the type attribute is in the toolbar state) object (if the usemap attribute is present) select textarea video (if the controls attribute is present)

If it does work in some browsers it's just because they're trying to play nice with malformed markup and provide some sort of meaningful result.

In other words: rewrite your HTML, it's a mess. If you want the links to look like they're in a button, put them in a div element and style that to look like one, instead of abusing semantically wrong elements for it.

<a> is not allowed inside <button>

Phrasing content, but there must be no interactive content descendant.

<a> is interactive content (regardless of whether it has an href apparently, but yours do). Thus you can't depend on having the links as children of the button and what Firefox is doing is correct. Use another element to contain the <a>s