blockui over jQueryUI modal dialog

You don’t specify what you have tried with z-index.

The blockUI plugin has an option to change the z-index of the message it creates (documentation):

// z-index for the blocking overlay 
baseZ: 1000,

jQuery UI Dialog as an option for specifying a z-index as well. Its default value is 1000. So you have to set a higher number for the BlockUI option, let’s say 2000:

$.blockUI({
    theme: true,
    baseZ: 2000
})

DEMO