"but the 'getkey()' holds the program execution."

so write one that doesn't!

or write a function which checks for available received character(s), and then only call getkey when there's something to get; eg,

if( rx_available() )
{
    rx_char = getkey();
}

That's what I do!

There's an interrupt-driven serial IO example in the Keil downloads area, and Mark Odell has published his free UART driver both here and on the Keil forum.