When working with ggplot2, I also found useful the ggdraw() function from the cowplot package as showed here.
Here is an example:
library(ggplot2)
library(gridExtra)
# Create two plots
p1 <- ggplot(mtcars, aes(hp, mpg)) +
geom_point() +
theme(plot.background = element_rect(fill="wheat1", color = NA))
p2 <- ggplot(mtcars, aes(hp, drat)) +
geom_point() +
theme(plot.background = element_rect(fill="wheat1", color = NA))
# stitch them together
g <- grid.arrange(p1, p2, nrow = 1)
# final touch
g2 <- cowplot::ggdraw(g) +
theme(plot.background = element_rect(fill="wheat1", color = NA))
# check the plot
plot(g2)
# save it as png
ggsave("img/plot-background.png", g2)

While p1 and p2 have already the plot.background fill set, there remains a thin line between them that disappears when wrapping the grid.arrange with cowplot::ggdraw using the same fill. As if you stitch two tiles together and then brush over the final layer of paint.