updated main()

int main()
{
    enum {performNothing, performButton1, performButton2, performButton3};

    bool wasEitherButtonPressed = false;
    int  performFunc = performNothing;

    while (true) {

        // Capture current button state
        bool isB1Pressed = (button1 == 1) ? true : false;
        bool isB2Pressed = (button2 == 1) ? true : false;
        bool isEitherButtonPressed = isB1Pressed || isB2Pressed;

        // If either one or both buttons are pressed after neither
        // being pressed, pick a new function to perform.
        if (!wasEitherButtonPressed && isEitherButtonPressed) {
            if(isB1Pressed && isB2Pressed) {
                performFunc = performButton3;
            } else if (isB2Pressed) {
                performFunc = performButton2;
            } else {
                performFunc = performButton1;
            }
        }

        // Perform the same function (until a new button press)
        if (performFunc == performButton1) {
            button_1();
        } else if (performFunc == performButton2) {
            button_2();
        } else if (performFunc == performButton3) {
            button_1and2();
        }

        // Remember the button state for the next time around the loop

        wasEitherButtonPressed = isEitherButtonPressed;
    }
}

void main() {
    BusIn nibble(p5, p6);   // whatever port pins you want. bit0:p5, bit1:p6 
    uint8_t last = 0x03 & nibble;        // capture an initial state to compare 2. use ~nibble if active low

    while (true) {
        Thread::wait(20);                // We'll use 20 msec as the sample interval. Might want 40 msec
        uint8_t curState = 0x03 & nibble;    // use ~nibble if active low
        if (curState == last) {
            switch(curState) {
                case 1:  // only p5
                    p5Function();
                    break;
                case 2:  // only p6
                    p6Function();
                    break;
                case 3:  // p5 and p6
                    p56Function();
                    break;
                case 0:  // nothing pressed
                    break;
                default:  // anything unexpected
                    break;
            }
        } else {
            // they are different, do nothing.
        }
    }
}

void main() {
    BusIn nibble(p5, p6);   // whatever port pins you want. bit0:p5, bit1:p6
    uint8_t last = 0x03 & nibble;        // capture an initial state to compare 2. use ~nibble if active low
    int sampleCount = 5;

    while (true) {
        Thread::wait(10);                // We'll use 10 msec as the basic sample interval, and sampleCount multiples for full debounce
        uint8_t curState = 0x03 & nibble;    // use ~nibble if active low
        if (curState == last) {
            if (sampleCount) {
                sampleCount--;
                continue;
            }
            switch(curState) {
                case 1:  // only p5
                    p5Function();
                    break;
                case 2:  // only p6
                    p6Function();
                    break;
                case 3:  // p5 and p6
                    p56Function();
                    break;
                case 0:  // nothing pressed
                    break;
                default:  // anything unexpected
                    break;
            }
        } else {
            // they are different, reset the counter.
            sampleCount = 5;
        }
    }
}