You can't combine the plots because (as per the documentation) heatmap() uses layout and draws the image in the lower right corner of a 2x2 layout. Consequentially, it can not be used in a multi column/row layout, i.e., when par(mfrow = *) or (mfcol = *) has been called.
Your best best would be to use ggplot2 and gridExtra to combine the graphs. For this both the heatmap and bar plot need to be created using ggplot.
You can find a heatmap on ggplot2 tutorial here.
Once you have your two plots combine them using the following commands:
#Create the plots
g1 <- heatmap
g2 <- barplot
#Arrange them in a grid
gg1 <- ggplot_gtable(ggplot_build(g1))
gg2 <- ggplot_gtable(ggplot_build(g2))
grid.arrange(gg1, gg2, ncol=2)