We do the layered emergency fund ourselves. In case of needing money in a hurry we'd tap cash accounts, readily available credit, break CDs, sell bond, cash out taxable investments as needed (have never needed to do any of this).
We do keep relatively sizeable amounts (a few months worth to a year of expenses) in cash accounts and bond, and I count them towards the fixed income portion of my overall portfolio.
Since you mentioned you only have a "baby" emergency fund, maybe you should keep it all in cash until it grows large enough, then put extra money into something slightly less liquid.