I don't use either of those browsers myself, but in common with most browsers, somewhere in their settings they have a tick box for "Allow pages to choose their own fonts" which is usually selected by default. Before you start redesigning your website I would check to see if that option is still selected in your versions of Epiphany and Midori.
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).